Related papers: Uncertainty functionals revisited: Concavity and J…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the…
Meaningful uncertainty quantification in computer vision requires reasoning about semantic information -- say, the hair color of the person in a photo or the location of a car on the street. To this end, recent breakthroughs in generative…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6,…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring…
Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models; to estimate model errors and thereby improve predictive capability; to…
We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…
The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite…
We develop a new framework for the Jensen-type inequalities that allows us to deal with functions not necessarily convex and Borel measures not necessarily positive.
One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behaviour (cf. Heckman 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
A real valued function defined on}$\mathbb{R}$ {\small is called}$g${\small --convex if it satisfies the following \textquotedblleft generalized Jensen's inequality\textquotedblright under a given}$g${\small -expectation, i.e.,…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
Recently several European National Measurement Institutes have established traceable calibration methods for dynamic mechanical quantities, e.g., dynamic force, torque and pressure. However, the use in industry and elsewhere of dynamic…
Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…
We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…
We present an online and data-driven uncertainty quantification method to enable the development of safe human-robot collaboration applications. Safety and risk assessment of systems are strongly correlated with the accuracy of…